Boyer et al., Anatomical Record

78 Pages·2014·23.2 MB·English

Title: A new fully automated approach for aligning and comparing shapes
Doug M. Boyer1,3, Jesus Puente2, Justin T. Gladman3,4, Chris Glynn5, Sayan Mukherjee5-
7, Gabriel S. Yapuncich1, Ingrid Daubechies7
1Department of Evolutionary Anthropology, Duke University

2Program In Applied and Computational Mathematics, Princeton University
3NYCEP, New York Consortium in Evolutionary Primatology
4PhD Program in Anthropology, CUNY Graduate Center
5Department of Statistical Science, Duke University
6Department of Computer Science, Duke University
7Department of Mathematics, Duke University

Short Title: Automated 3D Geometric Morphometrics

Keywords: auto3dgm, minimum spanning tree, R-package, iterative closest points,
morphological disparity, transformational homology

Manuscript breakdown
Text pages: 42 (12 font, Times New Roman, double-spaced)
References pages: 11 (12 font, Times New Roman, double-spaced)
Figures: 12
Tables: 6
Supplemental Figures: 3
Supplemental Tables: 4

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Abstract
Three-dimensional geometric morphometric (3DGM) methods for placing
landmarks on digitized bones have become increasingly sophisticated in the last 20 years,
including greater degrees of automation. One aspect shared by all 3DGM methods is that
the researcher must designate initial landmarks. Thus, researcher interpretations of
homology and correspondence are required for and influence representations of shape.
We present an algorithm allowing fully automatic placement of correspondence points on
samples of 3D digital models representing bones of different individuals/species, which
can then be input into standard 3DGM software and analyzed with dimension reduction
techniques. We test this algorithm against several samples, primarily a dataset of 106
primate calcanei represented by 1,024 correspondence points per bone.
We compared results of our automated analysis of these samples to a published
study using a traditional 3DGM approach with 27 landmarks on each bone. Data were
analyzed with morphologika2.5 and PAST. Results show strong correlations between
principal component scores, similar variance partitioning among components, and
similarities between the shape spaces generated by the automatic and traditional methods.
While cluster analyses of both automatically generated and traditional datasets produced
broadly similar results, there were also differences. Overall these results suggest to us
that automatic quantifications can lead to shape spaces that are as meaningful as those
based on observer landmarks, thereby presenting potential to save time in data collection,
increase completeness of morphological quantification, eliminate observer error, and
allow comparisons of shape diversity between different types of bones. We provide an R
package for implementing this analysis.

Introduction
As the theme of this volume is the application of three dimensional (3D) geometric
morphometrics (GM) to functional morphology, there is little need to convince most
readers about the importance of morphological studies to evolutionary and developmental
biological research. However, the utility of detailed morphological information in such
research has become increasingly questioned (see Springer et al. [2013] comment on
O’Leary et al. [2013a, b]). Therefore, we would like to emphasize that patterns of
phenotypic variation (including morphology) among biological structures form the basis
for understanding gene function (e.g., Morgan, 1911; Abzhanov et al., 2006),
developmental mechanisms (e.g., Harjunmaa et al., 2012), ecological adaptation (e.g.,
Losos, 1990; Frost et al., 2003), and evolutionary history (e.g., Leakey et al., 1964;

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Ostrom, 1975; Gingerich et al., 2001). Given its importance in a diverse set of biological
disciplines, we believe that morphological information remains highly relevant to
scientific discovery and advancement.
Since the Modern Synthesis of Evolutionary Theory was reached in the 1940s and
evolution was appropriately re-defined in its most basic population-genetic context,
genomic approaches to studying evolution have exploded. In part, this sea change is a
result of increasingly available data and improving computational power. Ever more
comprehensive and rapid assessments of genetic variation have been possible as a result
(Venter et al., 2003). Since the late 1980s, large-scale automated genomic analyses have
flourished and a great deal is now known about genotypic variation (McVean et al., 2005;
Houle et al., 2010). Genetic data are even accessible from remains of extinct organisms
such as subfossil lemurs (Orlando et al., 2008) and Neandertals (Green et al., 2010).
The utility of morphology is now questioned, in part, because the ability to analyze
morphological data has progressed much more slowly than the ability to analyze genomic
data. However, there is a call from some evolutionary biologists for the collection and
analysis of high-dimensional phenotypic data (Houle et al., 2010) in an analogous high-
throughput and automated fashion. This perspective proposes that the utility and
information content of genetic data will only reach its fullest extent once data on
associated phenotypes can be analyzed at equivalent rates and scales. Ideally, increasing
availability of phenomic data would promote comprehension of how the interaction
between phenotypic variation and the environment is mediated by the genome and how
selective pressures on the phenome are transferred to the genome. Reflecting the
perceived importance of such data, the field of phenomics has recently been defined as

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that endeavoring to acquire high-dimensional phenotypic data on an organism-wide scale
(Houle et al., 2010). Although phenomics is defined in analogy to genomics, the analogy
is misleading in one respect. We can come close to characterizing a genome completely
but not a phenome, as the information content of phenomes dwarves genomes and is
heavily influenced by the mode, tempo, duration, and timing of its observation and
quantification (Houle et al., 2010).
By itself, variation in morphological structure (a component of phenomic variation)
has higher dimensionality than variation in the genome, which makes it exponentially
more difficult to quantify in a meaningful way (e.g., Boyer et al., 2011). This is not to say
that significant advances in analysis of morphology are impossible or that the field of
morphometrics has stagnated. As emphasized and demonstrated by work in this volume,
new and more sophisticated approaches are being developed. More sophisticated
statistical contexts (Nunn, 2011) are available thanks to improved computing power and
flexible open-source coding languages (Orme et al., 2011; R Coding Team, 2012).
Additionally, there is growing automation of shape quantification based on new
variations of methods for spreading semi-landmarks over a 3D surface model (Bookstein,
1997; Bookstein et al., 1999; Bookstein et al., 2002; Perez et al., 2006; Harcourt-Smith et
al., 2008; Mitteroecker and Gunz, 2009). However, 3D shape analyses are generally tied
to at least two-user determined landmarks (Polly and MacLeod, 2008), and 3DGM
analyses do not appear to be very meaningful without four or more (Gunz et al., 2005;
Wiley et al., 2005). As a result, these approaches continue to have many of the same
limitations as morphological studies from 30-40 years ago. Part of the problem is sample
size; in most cases the number of measurements, and the sample sizes per study have

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changed little (compare Berge and Jouffroy [1986] to Moyà-Solà et al. [ 2012] – though
statistical analyses are more sophisticated in the more recent study, there are no
substantial differences in measurement complexity or sample sizes in these two studies
almost 30 years apart). Other principal limitations to the current traditional approach to
morphological studies include: 1) subjectivity/observer-error in interpretation and
measurement, 2) time intensiveness for generating large datasets, 3) sparse and
potentially incomplete and/or biased representation of specimen morphology and sample
variation, and 4) limited accessibility of information encapsulated in morphology due to
lack of widespread researcher expertise. All restrictions stem from the necessity that
researchers must directly observe, interpret, and actively measure (or mark) every
specimen of a study. These limitations may explain why genetic data currently provide a
more statistically powerful approach to certain evolutionary questions, and also why
questions that can be addressed only by morphology (e.g., what physical traits are
functionally beneficial for a certain behavior?) are often less thoroughly examined or
appear more controversial despite long histories of analyses.
As discussed by MacLeod et al. (2010), in order to make the study of morphology
less of a “cottage industry” and bring it to a new level of objectivity, standardization,
efficiency, and accessibility, we should seek more automation in the determination of
patterns of morphological similarity and difference. Several researchers (Lohmann, 1983;
MacLeod, 1999; Polly and MacLeod, 2008; Sievwright and MacLeod, 2012) have
worked to develop techniques that minimize assumptions involved in measuring shape
similarity. Initiatives for “automated taxonomy” exist (Weeks et al., 1999; MacLeod,
2007) and have had some degree of success. However, all of these automated approaches

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require a “dimension reduction” in the initial analytical stages, which still necessitates
that the researcher to make a decision, informed by their understanding of important and
“equivalent” morphological features on how to make that reduction. Most automated
work has been carried out on 2D outlines or raster-photographs. In such cases, the shape
of an outline and the images in a photograph are determined by how the researcher
orients the camera with respect to the specimen. Even when attempting the “same” view,
two different researchers may have systematic error with respect to one another or
different levels of random error in setting up specimens for photography. Furthermore,
many techniques described as automated, including those for 2D objects, still require
direct interaction with the study materials to determine at least one “corresponding point”
common to all the shapes of the study sample (see papers in MacLeod, 2007).
Biomedical and neuroscience research pursued by computer scientists has led to some
successful automated quantification procedures in 3D (Styner et al., 2006; Paniagua et al.,
2012). However, these methods have been designed with a limited range of variation in
mind and applied to monospecific samples. Whether these methods would have
meaningful success in a sample with more substantial shape diversity among homologous
objects is unknown.
In order to begin testing the limits on the degree to which, and the questions for
which shape analysis can be automated towards a scientifically meaningful end, we
present a new fully automated algorithm for aligning digital 3D models of bones and
placing landmarks comprehensively on them. We also provide an R package application
to promote its testing and use by other researchers. This method builds conceptually on a
previously published approach (Boyer et al., 2011) where it was shown that a

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superficially similar algorithm can 1) reasonably match corresponding points on different
instances of the same bone (represented by different individuals and species), 2) estimate
shape differences that allow classification of shapes to species with accuracy comparable
to, or better than, user selected landmarks on the same specimens, and 3) allow for the
entertainment of different “correspondence hypotheses” based on the morphocline (or
“path”) that is assumed to connect shapes in the dataset. Operationally, the method of
Boyer et al. (2011) finds several hundred candidate alignments between conformally-
flattened representations of two objects. Each initial alignment is “improved” using a thin
plate spline to align automatically identified extremal points (points of high local
curvature – i.e., “type II landmarks”). These mappings are then applied to unflattened
versions of the two objects and a continuous Procrustes distance is computed (Lipman
and Daubechies, 2010). The mapping that results in the minimum continuous Procrustes
distance is treated as the best mapping among the many candidate maps. This minimum
distance mapping was found to usually represent a biologically meaningful alignment
according to criteria 1 and 2 described above.
Despite its successes, the method presented by Boyer et al. (2011) has several
shortcomings: 1) since correspondences used to determine shape differences are purely
pairwise and not transitive, there is an inconsistent template for biological
correspondence relating all pairs of shapes in the dataset); 2) the conformal flattening
procedure of the analysis limits its application to “disc-type” shapes with an open end
(like the tooth crowns or ends of long bones of that dataset); and 3) the MATLAB®
application for the analysis is difficult to work with, lacks good visualization tools, and
does not yield output that can be widely employed in other analytical procedures.

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We overcome these limitations in the new algorithm presented here, which we have
developed into an R-package called auto3dgm. One of the most exciting prospects of
auto3dgm is its potential to help quantify morphology more comprehensively and
equably (if not exhaustively). It has long been acknowledged that measurements of select
characters are less meaningful than more comprehensive approaches:

“Direct determination of rate of evolution for whole organisms, as
opposed to selected characters of organisms, would be of the greatest
value for the study of evolution. Matthew wrote, nearly a generation ago
(1914), ‘to select a few of the great number of structural differences for
measurement would be almost certainly misleading; to average them all
would entail many thousands of measurements for each genus or species
compared.’” (Simpson, 1944: pg.14)

“Another level of description -of entire surface regions, or of volumetric
elements, or of qualitative aspects of structures rather than structures
themselves- may in some instances be most meaningful (Roth, 1984,
1991) and bring us closer to identifying the biological processes of
interest. Hence the appeal and utility of methods of comparison that
interpolate between landmark points, such as D'Arcy Thompson's
transformation grids” (Roth, 1993: pg. 53)

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Matthew’s implied perspective was that increasing the number of measurements
would be useful (though impractical) and would approach a representation of the “total
taxonomic distance.” This taxonomic distance is sometimes referred to as “morphological
disparity” and may allow meaningful discussion of the amount, rate and pattern of
evolution among a sample of species in certain settings. A greater amount of
morphological difference between corresponding and homologous structures is assumed
to relate to the amount of evolutionary change that has occurred in the compared taxa
since they diverged from their common ancestor. This idea is reflected in the numerical
taxonomy movement (Sokal, 1966; Sneath and Sokal, 1973).
A wealth of careful, mathematically-rooted consideration has been aimed at these
premises over the years. It has been effectively argued that it is actually impossible to
generate a generalized comprehensive view of the total phenetic distance between
specimens or taxa (Bookstein, 1980; Bookstein, 1994; MacLeod, 1999). In fact,
Bookstein (1991; 1994) argues that morphometrics is purely about documenting
covariance among biological forms, stating that morphometric methods are neither suited
for “the computation of ‘magnitude’ of shape change nor for the clustering of individual
specimens according to degree of similarity of shape” (Bookstein, 1994, p.205).
MacLeod (1999) explains the insufficiency of morphometrics in this regard, saying: “All
morphological disparity estimates published thus far represent indices that are
inextricably tied to particular methods of morphological representation and particular
scales of morphological assessment”, that “it seems…unlikely that a generalized estimate
of ‘morphological disparity,’…can ever be achieved.” and finally that it is imperative that

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“the morphometrician remembers the domain within which he/she operates is strictly
limited” (MacLeod, 1999, p.134).
We do not suggest the method we present fundamentally resolves any of these issues.
It aids in the discussion of morphological disparity because it is more objective and
comprehensive in its measurement of shape than previous methods. Though Bookstein
(1994) argues that morphometrics must be applied after homology considerations have
taken place, we suggest that our method can help identify an “operational homology” or
“biological correspondence” (Smith, 1990) more objectively.
Of the various types of homology discussed by evolutionary biologists and
paleontologists, it is relevant to review at least three different types here: these include
transformational, operational, and taxic homology (Patterson, 1982; Smith, 1990). It
would seem that transformational homology is of primary importance in an evolutionary
sense. It is similar to Darwinian homology (Simpson, 1961), in which features are
considered homologous among several taxa if they are equivalent through “descent with
modification” from the common ancestor. This also matches Van Valen’s (1982)
definition of homology as “continuity of information” through evolution. Of course,
comprehension of transformational homology is often fairly elusive, since the
morphoclines describing it can be expected to gain accuracy with a more complete fossil
record and an accurate phylogeny of life (Van Valen, 1982).
Operational homology most generally appears to refer to ontologies defining
biological correspondence for the sake of measurement, comparison among taxa, and/or
as a working hypothesis of transformational homology. What Macleod (2001, p.3)
describes as “geometric (or morphometric) homology (sensu Bookstein 1991)” of

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